Question

The ratio $\dfrac{{\sin i}}{{\sin r}}$ where $\angle i$ and $\angle r$ are the angles of incidence and refraction respectively is called the ________ of the second medium (B) with respect to the first medium (A).
A. optical density
B. power
C. refractive index
D. none

Answer 1

Hint: Use the Snell’s Law when refraction occurs to find the relationships between the angles of incidence, refraction and refractive indices of the two media. Try to understand the definitions of each of these options.

Complete answer:
First let us look at the definitions and formulas of the options given.
A. Optical Density: Transmission of light through a medium involves interactions between fundamental particles such as electrons, atoms, and ions. Absorption occurs as a beam of light interacts with absorbing atoms. It is determined by the thickness of the sample and the concentration of absorbing atoms. Optical density is defined to be the logarithm of the reciprocal of the transmittance of the medium for a particular wavelength \[{\log _{10}}\left( {\dfrac{1}{{{T_\lambda }}}} \right)\] where T is the transmittance.

B. Optical power: The degree to which a lens, mirror, or other optical system converges or diverges light is referred to as optical power. It is equal to the inverse of the device's focal length $P = \dfrac{1}{f}$. A short focal length leads to a high optical power. The inverse metre (${m^{ - 1}}$), also known as the dioptre, is the SI unit for optical power.

C. Refractive index: The refractive index of a material is a dimensionless number that expresses how fast light travels through the material. It is defined as $n = \dfrac{c}{v}$, where c is the speed of light in vacuum and v is velocity of light in the medium. If there are two medias the ratio of their respective refractive indices is called as the refractive index of first medium 1 with respect to the second medium 2.

Now, we know from Snell’s Law that when refraction takes place the ratio $\dfrac{{\sin i}}{{\sin r}}$ where $\angle i$ and $\angle r$ are the angles of incidence and refraction, is equal to the ratio $\dfrac{{{n_B}}}{{{n_A}}}$ which is the refractive index of medium B with respect to medium A. So, refractive index is the correct option.

Hence the correct option is C.

Note: We can easily get confused with the formulas for the relative refractive index. Remember that optical density depends on both the nature and shape of the material whereas refractive index depends on only the nature of the material (apart from the wavelength of light as both of them depend on it).